1.

The accompanying
diagram shows the

graph of the
distance travelled by

by each of
two cars, A and B.

1.1

Describe the
motion of car A

for the first 2 hours, i.e. from t = 0 to t = 2

1.2

What
happens at point P?

1.3

At what speed
does car A travel

for the first 2 hours?

1.4

Which car
travels at the higher speed

from t = 0 to t = 2? Explain.

1.5

At what
average speed does car A travel from t = 0 to t = 3 hours? Explain.

1.6

At what
average speed does car B travel from t = 0 to t = 3 hours?

1.7

Is there a
a time when the cars travel at the same speed? Explain.

1.8

Both
cars travel at the same average speed for the journey, i.e. from t = 0 to t = 6 hours.

Do you
agree? Explain.

2.

The accompanying
diagram shows the graph

of f: y = 2x + 3 .

2.1

Calculate
the value of y if x = –2 and x = 8.

2.2

Calculate the
value of x if y = 4 and if y = –5

g is
a second line defined by y = 18 – 0,5x

2.3

Calculate the
value of y on g if x = –2 and if x = 8.

2.4

Calculate the
value of x on g if y = 17 and if y = 13.

2.5

Calculate the
co-ordinates of P, the point of

intersection of f and g.

2.6

Say
which of the following statements is true and give a reason:

If x = –2 then (a) 2x + 3 = 18 – 0,5x ** OR **
(b) 2x + 3 < 18 – 0,5x **
OR ** (c) 2x + 3 > 18 – 0,5x

2.7

Say
which one of the following statements is true and give a reason:

If x = –2 then (a) f = g ** OR ** (b) f < g **
OR ** (c) f > g .

2.7

Repeat
2.6 but with x = 8.

2.8

Say for
which value(s) of x will (a) f < g (b) f = g (c) f > g

2.9

M(–2 ; –1)
is a point on f and N(–2 ; 19) is a point on g. Write down the length of line MN.

2.10

Now write down
the value of f – g if x = –2.

2.11

Calculate
the value of f – g if x = 8 ; x = 0,5 and x = –4,5.

2.12

For which value(s)
of x will f = 0 ; f < 0 ; f > 0

2.13

For which value(s)
of x will f.g < 0 ** OR ** f.g = 0 ** OR **
f.g > 0

3.

The diagram
shows the graph, f, of the income

realized by selling n items and the

graph, g, of the cost to manufacture the n items.

The graphs
f and g intersect at P.

3.1

Why does
the line f start in the origin (0 ; 0)?

3.2

The
graph of g does not start in the origin.

Explain.

3.3

When is
a profit made? Use the graphs f and g

to answer the question.

3.4

Read
from the graph the income made from the sale of 4 items.

3.5

Show
that the gradient of the line f is 1,5.

3.6

The graph
of f passes through the origin (0 ; 0). Write down the equation of the line f.

3.7

The
equation of line g is y = 0,875x + 5. Show that P, the point of intersection of f and g,

is the
point (8 ; 12).

3.8

Is a
profit made if

3.8.1

8 items are sold?

3.8.2

less than 8 items are sold?

3.8.3

more than 8 items are sold?

3.9

How much
profit is made from the sale of 4 and 10 items?

3.10

The
profit made must be at least R2,5. How many items must be sold?